The header of your shop contains for instance the logo of your shop, the main menu and the search function. It is the same on every page of your shop. The only exception are the pages of the checkout (see below).
The main menu consists of links to your home page, to all category pages and content pages.
The design of the header depends on the theme you chose. You can find more information on this in the article Using themes / design templates.
It is possible to display the unique selling points or main customer advantages of your shop in the header. If you offer free shipping for instance, you can then mention this in the header. You can find more information on this in the article Unique selling points (USPs) in the header of your shop.
The header in the checkout
During the checkout the normal header of your shop is not shown anymore. Instead the header only contains the logo/name of your shop, a link that is leading back to the cart and navigation for the steps of the checkout. The reason for this is that the customer should not be distracted during the checkout.